I believe the biggest space mission of the twenty-first century will be a manned mission to Mars, and the colonization that follows. This is the stated goal of several nations, companies, and individuals, all with considerably deep pockets. This mission will not only be a huge leap forward in space exploration, it will usher in a new era in human history in which the human race is an interplanetary civilization, a natural milestone as humanity continues to progress and advance.
Significant challenges are many and overwhelming. In terms of getting to mars, we need efficient, powerful propulsion systems and a spaceship that can not only accommodate a full crew for a mission that would likely last years, but withstand the various hazards that a long trip through space and entrance into the Martian atmosphere will entail. In terms of colonization, significant challenges will include establishing efficient and frequent travel/transport between the planets, and in the longer term, the necessity to terraform the planet (make it more like Earth) so that humans can more easily live there.
